The effect of variability in the powder/liquid ratio on the strength of zinc phosphate cement

Aim: To investigate (a) variability in powder/liquid proportioning (b) effect of the extremes of any such variability on diametral tensile strength (DTS), in a commercial zinc phosphate cement. Statistical analyses (a = 0.05) were by Student's t-test in the case of powder/liquid ratio and one-way ANOVA and Tukey HSD for for pair-wise comparisons of mean DTS. The Null hypotheses were that (a) the powder-liquid mixing ratios observed would not differ from the manufacturer's recommended ratio (b) DTS of the set cement samples using the extreme powder/liquid ratios observed would not differ from those made using the manufacturer's recommended ratio. Methodology: Thirty-four undergraduate dental students dispensed the components according to the manufacturer's instructions. The maximum and minimum powder/liquid ratios (m/m), together with the manufacturer's recommended ratio (m/m), were used to prepare cylindrical samples (n = 3 x 34) for DTS testing. Results: Powder/liquid ratios ranged from 2.386 to 1.018.The mean ratio (1.644 (341) m/m) was not significantly different from the manufacturer's recommended value of 1.718 (p=0.189). DTS values for the maximum and minimum ratios (m/m), respectively, were both significantly different from each other (p<0.001) and from the mean value obtained from the manufacturer's recommended ratio (m/m) (p<0.001). Conclusions: Variability exists in powder/liquid ratio (m/m) for hand dispensed zinc phosphate cement. This variability can affect the DTS of the set material.

Catalyst, additive and substrate effects in intramolecular aromatic additions of alpha-diazoketones

This thesis is focused on transition metal catalysed reaction of α-diazoketones leading to aromatic addition to form azulenones, with particular emphasis on enantiocontrol through use of chiral copper catalysts. The first chapter provides an overview of the influence of variation of the substituent at the diazo carbon on the outcome of subsequent reaction pathways, focusing in particular on C-H insertion, cyclopropanation, aromatic addition and ylide formation drawing together for the first time input from a range of primary reports. Chapter two describes the synthesis of a range of novel α-diazoketones. Rhodium and copper catalysed cyclisation of these to form a range of azulenones is described. Variation of the transition metal catalyst was undertaken using both copper and rhodium based systems and ligand variation, including the design and synthesis of a novel bisoxazoline ligand. The influence of additives, especially NaBARF, on the enantiocontrol was explored in detail and displayed an interesting impact which was sensitive to substituent effects. Further exploration demonstrated that it is the sodium cation which is critical in the additive effects. For the first time, enantiocontrol in the aromatic addition of terminal diazoketones was demonstrated indicating enantiofacial control in the aromatic addition is feasible in the absence of a bridgehead substituent. Determination of the enantiopurity in these compounds was particularly challenging due to the lability of the products. A substantial portion of the work was focused on determining the stereochemical outcome of the aromatic addition processes, both the absolute stereochemistry and extent of enantiopurity. Formation of PTAD adducts was beneficial in this regard. The third chapter contains the full experimental details and spectral characterisation of all novel compounds synthesised in this project, while details of chiral stationary phase HPLC and 1H NMR analysis are included in the appendix.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.